Abstract
ABSTRACT An analogue of the convergence part of Khintchine’s theorem (1924) for simultaneous approximation of integral polynomials at the points (x1, x2, z,w) ∈ R2 × C × Qp is proved. It is a solution of the more general problem than Sprindźuk's problem (1980) in the ring of adeles. We use a new form of the essential and nonessential domain methods in metric theory of Diophantine approximation
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